Gravitational radiation in higher order non-local gravity

Abstract

In this paper, we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density [Formula: see text]. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for [Formula: see text], corresponding to the angular frequency [Formula: see text], composed of two standard [Formula: see text] and [Formula: see text] polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and [Formula: see text], an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of [Formula: see text] modes associated to [Formula: see text] angular frequencies [Formula: see text], each of which is of breathing polarization [Formula: see text] to lowest order in [Formula: see text], a parameter that takes into account the difference in speed between the slightly massive wave and the massless one. Thanks to NP formalism, we find that the [Formula: see text] class of non-local gravitational waves is [Formula: see text], according to Petrov classification, where the presence or absence of all modes are observer independent. Also, the scalar radiation is forbidden for [Formula: see text] and [Formula: see text] cases, when some conditions are satisfied. Finally, in [Formula: see text] gravity where [Formula: see text], a possible degenerate case with a continuous infinity of transverse massive scalar breathing modes appears under a particular constraint, which reproduces in two-dimensional spacetime the Polyakov–effective action.